几何非线性非保守系统弹性动力学两类变量的广义拟变分原理的应用

非线性非保守系统弹性动力学的广义变分原理的研究,是一个相当重要的研究领域。它不仅在有限元素法和其它近似计算方法中得到广泛应用,而且可以方便地求得非线性非保守系统弹性动力学问题的精确解。文章应用几何非线性非保守系统弹性动力学中的第一类两类变量广义拟余能原理,研究了一个典型的非保守动力学系统边值问题的动态特性,并给出同时求解一个典型的几何非线性非保守系统的内力和变形两类变量的计算方法。

Application of generalized ouasi-variational principles with two kinds of variables in geometric nonlinear non-conservative elasto-dynamics

The research of generalized variational principles of nonlinear non-conservative elasto-dynamics is very vital.They are applied not only to FEM and other approximate calculating methods widely,but also to the accurate solution of nonlinear non-conservative elasto-dynamics conveniently.The dynamical property of boundary value problem of a typical non-conservative elasto-dynamics was studied by applying the generalized quasi-com-plementary variational principle of the first two kinds of variables in geometric nonlinear non-conservative elasto-dynamics,and the method of calculating the internal force and the deformation simultaneously was derived.